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Which of the following is the equation of a line that passes through the point (0, a) and has perpendicular distance a from the point (2a, 2a)?

1. 3x − 4y − 3a = 0
2. x − a = 0
3. Both (a) and (b)
4. Neither (a) nor (b)

Correct answer: Both (a) and (b)

Solution

Both candidate lines pass through (a,0) and lie at distance a from (2a,2a): for 3x-4y-3a=0 the distance is |6a-8a-3a|/5 = a, and for x=a the distance is |2a-a| = a. Hence both equations satisfy the condition.

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